RU2484484C2 - Electric energy consumption determination method - Google Patents

Abstract

FIELD: electrical engineering.

SUBSTANCE: electric energy consumption determination method includes the following sequence of actions: the signal being measured, that corresponds to the consumer AC and AC voltage, is subjected to integrated Fourier analysis, sampling frequency adjustment to the oscillating grid frequency of the energy distribution grid for which purpose one determines the corresponding principal oscillation vector

immediately from two consecutive periods of the signal measured, determines the phase angle (Δφ) confined between the both vectors which angle is applied during sampling frequency adjustment.

EFFECT: ensuring high accuracy of consumed electric energy determination at measurements sampling frequency adjusted to oscillating grid frequency.

2 cl, 2 dwg

Description

Technical field

The invention relates to a method for determining the consumption of electric energy that is supplied to a consumer by the energy distribution network, the measured signal that corresponds to the alternating voltage at the consumer is sampled with a sampling frequency and subjected to a comprehensive Fourier analysis, the sampling frequency tracking the oscillating network frequency of the energy distribution network.

State of the art

To measure the electrical energy that is supplied to the consumer by the energy distribution network, electronic meters are increasingly being used along with mechanical energy meters.

The electronic energy meter determines by sampling (sampling) the measured signal, which corresponds to the alternating voltage or alternating current supplied to the consumer, the time-discrete values of the samples, subjected them to complex Fourier analysis and determines, by multiplying the complex indicators of current or voltage, the delivered electrical power or electrical energy, and higher harmonics in the current or voltage signal are also taken into account.

In the energy distribution network, the main frequency or the rated frequency of the mains voltage has a predetermined value (in Europe, 50 Hz, in the USA 60 Hz). However, this rated frequency fluctuates, depending on the provided on the supplier's side and the current electrical instantaneous power received by the consumer. Under normal operating conditions, the allowable range of variation of the network frequency is set by means of the norms. The norm EN 50160 prescribes, for example, that a 10-second average value of the fundamental frequency can deviate by only 15% up or 15% down relative to 50 Hz.

For an electronic energy meter, this means that, at least within this given range of oscillations, the sampling frequency adapts to the oscillating network frequency, that is, it must be traceable. Only if the number of sampling times with respect to the main oscillation of the oscillating network frequency can be kept constant, the so-called “leakage effects” are prevented and the required measurement accuracy is achieved. In the absence of synchronization between the sampling frequency and the current network frequency, an unacceptably large error can occur in determining the consumption of electrical energy.

Along with constant changes in frequency, the electronic energy meter must also work out abrupt frequency changes that occur, for example, when the energy meter is turned on.

The upper and lower limits of a constant or spasmodic frequency change are set by the official party or through norms.

Tracking the sampling frequency can, for example, be implemented in such a way that the sampling frequency is derived from the frequency divider, and the latter is continuously adjusted depending on the frequency deviation. The premise is that the frequency deviation is known. In order to determine the frequency deviation, it is known that the transitions through zero of the network frequency are determined either using hardware or using software.

But in the energy distribution network, voltage and current are not purely sinusoidal, but may contain higher harmonics and / or a constant component.

Regarding the tracking of the sampling frequency, both the higher harmonics and the dc component create interference, since they cause the delay of transitions through zero. From the prolonged zero crossings only with high technical costs it is possible to derive the correct measure of the measure for sampling with sufficient accuracy.

In order to reduce the interfering influence of higher harmonics or a constant component in an electronic energy meter, it is known that these interference parameters are eliminated by means of (relatively steep) low-pass filters and band-pass filters.

Such filters, which can be implemented by hardware or software, increase the technical costs and, therefore, the cost of manufacturing an electronic energy meter.

Representation of the invention

The objective of the proposed invention is to propose a method for determining the consumption of electric energy, in which, as simple as possible, the sampling frequency can track the oscillating network frequency and high measurement accuracy can be achieved.

This problem is solved by a method with the features of paragraph 1 of the claims and an electronic energy meter with the features of paragraph 9 of the claims.

Preferred embodiments of the invention are defined in the dependent claims.

According to the main idea of the invention, in the electronic energy meter, continuously, from two consecutive periods of the measured signal, derived from the voltage, the phase difference of the main oscillation is determined by means of a complex Fourier analysis and is used as a clock measure to monitor the sampling frequency. A certain phase difference, i.e. a phase angle enclosed between two vectors, directly displays the frequency deviation. This means that if the network frequency is constant in two consecutive periods of the sampled measured signal, then the phase difference is zero. If, on the contrary, the network frequency experiences fluctuations, the measure of this oscillation is directly displayed in the magnitude of the difference angle between the two vectors of the main oscillation of the measured quantity. If the frequency deviation value is once set, then the phase angle can be converted to the corresponding digital value and can be applied in a known manner to the frequency divider, which accordingly adjusts the sampling frequency.

A significant advantage of the method according to the invention should be seen in the fact that the algorithm for determining the phase difference can be implemented relatively simply. No hardware or software is required for determining zero transitions. This simplifies the technical implementation of an electronic energy meter.

Preferred embodiments of the method according to the invention are used to track the sampling frequency, the phase angle, which is calculated using the equations (9), (11), (12a) and (12b) explained below.

Regarding the computational and technical costs, it can be advantageous if, when determining the phase difference, the quotient of the vector product and the scalar product is determined according to equation (9). Due to this, the error in determining electric energy can be kept very small even if the known approximation algorithms (series expansion) are used in the calculation of the arc tangent. As soon as the regulation is “fixed”, very small phase difference angles arise, which even with approximate calculation using the arctangent function can be determined quite accurately (arctan (x) ~ x for x << 1, and there is almost no inaccuracy in the calculation).

If a large width of the oscillations of the network frequency should be allowed, it can be favorable if, when converting by computer methods according to equation (9), the sum is formed in the denominator and the phase difference is calculated according to equation (11). Due to this, the "capture area" of the tracking algorithm increases.

So that also in cases where the network frequency changes by more than 25% with respect to the instantaneous frequency, it is possible to quickly achieve adaptation, in a particular embodiment of the invention, a distinction is made between the cases:

- if the scalar product is negative and a certain phase angle is greater than zero, then the clock measure for the sampling frequency is determined according to equation (12a);

- if the scalar product is negative and a certain phase angle is less than zero, then the clock measure for the sampling frequency is determined according to equation (12b). This reduces the execution time of the tracking algorithm and, therefore, the time to correct the sampling frequency.

A particularly favorable embodiment of the method according to the invention may differ in that the sampling frequency is output from the frequency divider, and a pre-divider is included before this frequency divider, and a digital parameter that corresponds to the phase difference is continuously fed to the pre-divider, and this parameter is consistent with the range +/- 19% of the rated frequency.

A particularly favorable correlation between computational and technical costs, computation speed and measurement accuracy can be achieved due to the fact that the period of the measured signal is sampled with 256 discrete values.

It is especially favorable if, when monitoring the sampling frequency, a larger range of fluctuations in the variation of the network frequency is covered than is provided for by the norm. Therefore, a particular embodiment of the invention is characterized in that the phase angle determined in accordance with the invention is limited by the oscillation range of +/- 19% of the network frequency relative to the network frequency corresponding to the energy distribution network. This is equivalent to reserve when tuning the sampling rate.

An electronic energy meter that is equipped with a computing device that implements program code according to the method of the invention can be manufactured relatively simply. Thus, it is possible with good accuracy and over a long service life to reliably measure the electrical energy supplied to the consumer.

Brief Description of the Drawings

For further explanation of the invention, reference is now made to the drawings, in which other preferred forms of execution, details and further development of the invention are presented and which show the following:

figure 1 is a vector representation of the main oscillations of the measured signal in two consecutive periods, and the measured signal corresponds to the voltage of the consumer in the energy distribution network, and moreover, according to the invention, the phase angle enclosed between the vectors (phase difference) is used to adjust the sampling frequency to an oscillating network frequency ;

figure 2 is a diagram in which the phase difference is shown in relation to the network frequency, and various variants of determining the phase angle according to the invention by means of the characteristic field are clearly illustrated, and the case of the nominal network frequency of 50 Hz is selected.

The implementation of the invention

As already noted above, the required accuracy of an electronic energy meter can be achieved only by the fact that the number of sampling points with respect to the main oscillation is kept constant, because otherwise, due to the so-called “leakage effect”, measurement inaccuracies would occur. In other words, the sampling frequency should be synchronized with the actual network frequency, that is, it will be tuned by regulation methods (frequency tuning). Typically, a software-defined frequency divider is used for this frequency adjustment, the output frequency of which serves as the sampling frequency, and the division coefficient allows for proper fine-tuning of the sampling frequency. An electronic energy meter determines energy consumption by sampling and Fourier analysis. If the instantaneous network frequency and the sampling frequency are slightly inconsistent, this affects the Fourier analysis in such a way that the vectors of the main oscillation of two consecutive periods rotate opposite to each other (see figure 1). The phase angle Δφ between both vectors provides an immediate criterion for the duration of the period and, therefore, for the current network frequency. The proposed invention uses this effect and applies a phase angle to fine-tune the sampling frequency. Since the phase angle is obtained from the discrete complex Fourier transform, it is hereinafter also referred to as the DFT phase angle.

From the point of view of the DFT control technique, the phase angle is the deviation of the controlled variable. The current network frequency can be considered as a setting parameter. The digital value supplied to the frequency divider from the (preliminary) divider functions as a control parameter.

Before explaining in more detail the various implementations of the method according to the invention based on modeling, mathematical principles will be presented.

. Оба вектора $$\overrightarrow{U}a$$

и $$\overrightarrow{U}n$$

являются результатом комплексного Фурье-анализа двух последовательных периодов измеренного сигнала, выведенного из сетевого напряжения. Вектор с индексом а обозначает при этом ранее дискретизированный период измеренного сигнала, а вектор с индексом n обозначает текущий дискретизированный период. Оба вектора непрерывно определяются из дискретизированных значений посредством Фурье-анализа.Figure 1 shows a representation of a complex plane with two vectors $$\overrightarrow{U}a,\overrightarrow{U}n$$

. Both vectors $$\overrightarrow{U}a$$

and $$\overrightarrow{U}n$$

are the result of a comprehensive Fourier analysis of two consecutive periods of the measured signal derived from the mains voltage. The vector with index a denotes the previously sampled period of the measured signal, and the vector with index n denotes the current sampled period. Both vectors are continuously determined from discretized values by Fourier analysis.

Equations (1) and (2) show the mathematical relationship to determine the real part a _{a, n} and the imaginary part b _{a, n of the} complex vector of the fundamental oscillation and the higher harmonic.

(one) (2)

For the main oscillation, k = 1.

From the real and imaginary parts of these vectors, it is possible to obtain the amplitude information and phase information of the measured signal (current or voltage) in a known manner and respectively to equations (3) and (4)

(3) (four)

From equation (4), the phase angle can be calculated from the individual angles of the vectors. But this is so costly from the point of view of computer technology, not least because of the decomposition of the arc tangent function in a series, the invention has chosen a different path.

In equation (5), the sine of the phase angle Δφ is represented as the vector product (×)

(5)

In equation (6), the cosine of the phase angle Δφ is represented as the scalar product ( ^o )

(6)

From (5) and (6) it follows the tangent of the phase angle Δφ as a quotient of the vector product and the scalar product

(7)

Based on these mathematical foundations, the method according to the invention is described in more detail below using simulation.

Figure 2 presents the phase difference (in radians) depending on the network frequency (in Hz). The abscissa represents the range of variation of the network frequency from 30 Hz to 70 Hz; characteristics 2, 3 and 4 clearly represent various implementations of the invention in this area.

If the network frequency deviates from the nominal network frequency within the oscillation range shown in FIG. 2 (from 30 Hz to 70 Hz), then this deviation is expressed as the phase difference between the vectors, which is shown in the “idealized” representation by characteristic 1. “Idealized” because that characteristic 1 reflects the actual phase deviation; it can be obtained by calculating or accurately measuring zero transitions. Characteristic 1 can be considered as an indication of a given value for the algorithm for adjusting the sampling frequency to an oscillating network frequency.

Compared to characteristic 1, characteristics 2, 3 and 4 show various characteristics of the phase angle change, which were obtained by modeling the algorithms of the invention (equation 9, 11, 12a and 12b) to determine the phase angle.

When modeling, for example, a sampling frequency of 12.8 kHz is used; this means 256 discrete values per period. The sampling rate is output from the frequency divider. The input frequency of the frequency divider is 133.3248 MHz (nominal division ratio 10.416), so that when changing the division coefficient a very accurate stepwise change in the sampling frequency is possible (in the range of 0.01%). In practice, it turned out that the above values of the exemplary embodiment represent a good compromise between the accuracy in measuring energy and the efficiency of the used computing and technical resources.

As can be seen from FIG. 2, in the region of small frequency deviations (i.e., in the region of the nominal frequency of 50 Hz), each of the phase angle DFT characteristics determined in accordance with the invention (characteristics 2, 3 and 4) gives a result that matches the characteristic 1. However, a significant advantage of the invention should be seen in the fact that the results 2, 3 and 4 can be achieved with a relatively very small software and hardware costs.

From equation (7), the phase angle Δφ is obtained according to the relation

(8)

According to a preferred embodiment of the invention, the phase angle Δφ is calculated according to the following equation (9)

(9)

A simulation of this calculation is shown in FIG. 2 using characteristic 2.

In this case, when calculating the length of the INT interval, the following equation (10) is applied in an arc measure:

(10)

If the network frequency does not change between both periods of the measured signal, then the length of the interval is 2π, since the phase angle Δφ is zero. On the contrary, if the network frequency fluctuates, then the phase angle Δφ is not equal to zero, and a digital value corresponding to the interval length is supplied to the frequency divider to generate a new (tuned) sampling frequency.

Within the range of oscillations from 40 Hz to 65 Hz, the simulated characteristic largely corresponds to the real characteristic 1. Outside this region from 40 Hz to 65 Hz, in the general case, this execution of the algorithm according to the invention according to equation (9) ceases to work. The reason is that when calculating the phase angle Δφ when the network frequency jump, which corresponds to a phase jump of more than π / 2, the sign of the phase angle DFT changes (as can be seen from figure 2, characteristic 2, for the case when the network frequency is less than 40 Hz, the regulation would be incorrect in the direction of higher frequencies; the corresponding is true for the network frequency to be regulated greater than 65 Hz). The invention solves this problem by the fact that equation (9) is modified so that instead of the scalar product of both vectors, the absolute value of the scalar product is applied (equation 11)

(eleven)

Due to this measure, an extended capture region can be realized when tuning the sampling frequency (frequency tuning), which corresponds to the phase tracking circuit. 2, this simulation result is represented by characteristic 3.

As can be seen from this characteristic 3 in Fig. 2, outside the region that corresponds to a phase jump in absolute value greater than π / 2, the DFT phase angle Δφ _mod1, although it now has the correct sign, now has an opposite directional characteristic (characteristic 3 decreases for frequencies below 40 Hz and increases for frequencies above 65 Hz, these areas can be recognized by the negative sign of the scalar product).

An improvement in the adaptation speed of the method according to the invention can be achieved by using case discrimination, and the calculated DFT phase angle Δφ _mod1 , in accordance with its sign, is subtracted from + π or -π.

This distinction is expressed in equations (12a) and (12b) as follows:

With this particularly preferred embodiment of the invention (Δφ _mod2 ), the best result can be achieved. As can be easily seen from FIG. 2, characteristic 4 calculated using equation (12a) or (12b) is closest to the ideal characteristic (tuning characteristic 1).

As mentioned above, according to EN 50160, a frequency deviation of +/- 15% from the nominal value of 50 Hz, i.e. from 42.5 Hz to 57.5 Hz, is required.

However, it is preferable if the reserve is implemented in the frequency adjustment and the operating range of +/- 19% is closed (i.e., from 40.5 Hz to 59.5 Hz).

The technical prerequisite for establishing these lower limit and upper limit is as follows: the theoretical boundary of this control algorithm for frequency jumps lies at +/- 50% with respect to the instantaneous frequency. This is due to the fact that from this boundary and when calculating the DFT angle of the phase difference according to equation (11) or equations (12a) and (12b), the sign would reverse. If, for example, when the electronic energy meter were turned on, the current frequency would be 30 Hz, then we should work out a frequency jump from 50 Hz (the initial frequency of the control algorithm after acceleration) to 30 Hz. Perhaps "adjustment" (bringing the error to zero or to a minimum) of this jump (-40% relative to 50 Hz). If then a backward jump from 30 Hz to 50 Hz occurred again, then the algorithm would generally stop working, since this deviation is more than 50% relative to 30 Hz. However, the above-mentioned boundaries guarantee that upon returning to the “work area” the adjustment is carried out without problems, namely, regardless of what value the frequency had before, and also regardless of where the jump is performed. In the proposed example, at a jump of 30 Hz, control would stop at the lower limit of 40.5 Hz, but a reverse jump of 50 Hz does not cause problems (even a jump to the upper limit would be possible). The boundaries were chosen in such a way that when jumping from the bottom up (this is a critical jump with a higher percentage deviation than from the bottom up), the deviation from the lower frequency was less than 50%.

As already mentioned above, FIG. 2 shows a case of a nominal network frequency of 50 Hz. In the case where the network frequency deviates from this nominal network frequency, for example, up to 45 Hz, the clock frequency is brought to this new “target frequency” of 45 Hz. As soon as this process of adjustment (adjustment) is completed, figure 2 should be read in such a way that on the abscissa the intersection point with characteristics 1-4 no longer corresponds to 50 Hz, but corresponds to 45 Hz. A similar condition is true, of course, if in the further process the network frequency deviates also from this new value of 45 Hz. In other words, if the network frequency continuously fluctuates, the abscissa in FIG. 2 needs to be continuously scaled again.

Designation of reference numbers used

1 - real ("idealized") characteristic (adjustment), a given frequency

2 - characteristic according to equation (9)

3 - characteristic according to equation (11)

4 - characteristic according to equations (12a) and (12b)

Claims (9)

1. A method for determining the consumption of electrical energy, which is supplied to the consumer by the energy distribution network, the measured signal that corresponds to the alternating voltage at the consumer is sampled with a sampling frequency and subjected to complex Fourier analysis, the sampling frequency being adjusted to the oscillating network frequency of the energy distribution network, at the same time, the corresponding vector is continuously determined from two consecutive periods of the measured signal

the main oscillation, determine the phase angle Δφ enclosed between both vectors and use the phase angle when adjusting the sampling frequency. 2. The method according to claim 1, characterized in that the phase angle Δφ used in the adjustment is determined according to the ratio:

Where
a _a is the real part of the first vector

,
b _a - imaginary part of the first vector

,
a _n is the real part of the second vector

,
b _n is the imaginary part of the second vector

, 3. The method according to claim 2, characterized in that when adjusting use the phase angle Δφ _mod1 , determined according to the ratio:

4. The method according to claim 3, characterized in that for the case of a frequency jump that corresponds to a phase jump of more than + π / 2, when adjusting, use the phase angle Δφ _mod2 , determined according to the ratio:

5. The method according to claim 3, characterized in that for the case of a frequency jump that corresponds to a phase jump of less than -π / 2, when adjusting, the phase angle Δφ _{mod2 is used} , which is determined according to the ratio:

6. The method according to claim 5, characterized in that the sampling frequency is generated by a frequency divider, with a preliminary divider included in front of the frequency divider, to which a digital value is applied that corresponds to a certain phase angle. 7. The method according to claim 6, characterized in that the period of the measured signal is sampled with 256 discrete values. 8. The method according to any one of claims 1 to 7, characterized in that the phase angle is limited by an oscillation range that corresponds to a deviation of +/- 19% of the network frequency associated with the energy distribution network. 9. An electronic meter of electrical energy, which contains a computing device that is configured to implement the method according to any one of claims 1 to 8.

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